Question

How do you simplify `(21-3x)/( 9x- 64x^3)`?

Answer 1

`(3(7-x))/(x(3-8x)(3+8x))`

Explanation:

`"factorise the numerator/denominator and cancel any"`
`color(blue)"common factors"`

`•color(white)(x)21-3x=3(7-x)larrcolor(blue)"common factor of 3"`

`•color(white)(x)9x-64x^3=x(9-64x^2)larrcolor(blue)"common factor of x"`

`"note that "9-64x^2color(blue)" is a difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=3" and "b=8x`

`rArr9-64x^2=(3-8x)(3+8x)`

`rArr(21-3x)/(9x-64x^3)`

`=(3(7-x))/(x(3-8x)(3+8x))to(x!=0,x!=+-3/8)`